In context, I guess your claim is: “if the ‘compressor’ is post-hoc trying a bunch of algorithms and picking the best one, the full complexity of that process should count against the compressor.” Totally agree with that as far as epistemology is concerned!
But I don’t think the epistemological point carries over to the realm of rational-fic.
In part that’s because I think of JKR-magic as in fact having a bunch of structure that makes it much easier to explain than it would be to explain a truly randomly-generated set of spells and effects (e.g. the pseudo-Latin stuff; the fact that wands are typically used). So I expect an retrofitted explanation wouldn’t be crazy tortured (wouldn’t require having a compression process that tests a ridiculous number N of patterns, or incorporates a ridiculous amount of fiat random bits).
In part I’m just making a tedious “nerds have different aesthetic intuitions about stuff” point, where I think a reasonably simple well-retrofitted explanation is aesthetically very cool even if it’s clearly not the actual thing used to generate the system (and maybe required a bunch of search to find).
I’m pretty uninformed on the object level here (whether anyone is doing this; how easy it would be). But crazy-seeming inefficiencies crop up pretty often in our fallen world, and often what they need is a few competent people who make it their mission to fix them. I also suspect there would be a lot of cool “learning by doing” value involved in trying to scale up this work, and if you published your initial attempts at replication then people would get useful info about whether more of this is needed. Basically, getting funding to do and publish a pilot project seems great. I’d recommend having a lot of clarity about how you’d choose papers to replicate, or maybe just committing to a specific list of papers, so that people don’t have to worry that you’re cherry-picking results when you publish them :)